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At least 19 records

The phase of the gravitational path integral

The gravitational path integral on S 2 × S 2 can be interpreted either as evaluating a contribution to the norm of the Hartle-Hawking wavefunction conditional on spatial S 1 × S 2 topology, or the pair creation rate of black holes in de Sitter. Both interpretations are distinguished at the quantum level. The former requires the path integral to be real and the latter to be imaginary. We develop a formalism to efficiently compute the phase of the gravitational path integral on Einstein spaces. We apply it to a broad class of spacetimes and in particular S 2 × S D−2 , finding it to be real and positive. We generalize some of the analysis to cases with charge and rotation.

AdS-CFT correspondence↗

On the lapse contour in the gravitational path integral

The gravitational path integral is usually implemented with a covariant action by analogy with other gauge field theories, but the gravitational case is different in important ways. A key difference is that the integrand has an essential singularity, which occurs at zero lapse where the spacetime metric degenerates. The lapse integration contour required to impose the local time reparametrization constraints must run from − ∞ to + ∞ , yet must not pass through zero. This raises the question: for an application—such as a partition function—where the constraints should be imposed, what is the correct integration contour, and why? We study that question by starting with the reduced phase space path integral, which involves no essential singularity. We observe that if the momenta are to be integrated before the lapse, to obtain a configuration space path integral, the lapse contour should pass below the origin in the complex lapse plane. This contour is also consistent with the requirement that quantum field fluctuation amplitudes have the usual short distance vacuum form, and with obtaining the Bekenstein-Hawking horizon entropy from a Lorentzian path integral. Published by the American Physical Society 2025

Banihashemi, Batoul (ORCID:0000000228679209)↗

Hollow-grams: generalized entanglement wedges from the gravitational path integral

Recently, Bousso and Penington (BP) made a proposal for the entanglement wedge associated to a gravitating bulk region. In this paper, we derive this proposal in time-reflection symmetric settings using the gravitational path integral. To do this, we exploit the connection between random tensor networks (RTNs) and fixed-geometry states in gravity. We define the entropy of a bulk region in an RTN by removing tensors in that region and computing the entropy of the open legs thus generated in the “hollowed” RTN. We thus derive the BP proposal for RTNs and hence, also for fixed-geometry states in gravity. By then expressing a general holographic state as a superposition over fixed-geometry states and using a diagonal approximation, we provide a general gravitational path integral derivation of the BP proposal. We demonstrate that the saddles computing the Rényi entropy Sn depend on how the bulk region is gauge-invariantly specified. Nevertheless, we show that the BP proposal is universally reproduced in the n → 1 limit.

2D Gravity↗

The gravitational path integral from an observer’s point of view

One of the fundamental problems in quantum gravity is to describe the experience of a gravitating observer in generic spacetimes. In this paper, we develop a framework for describing non-perturbative physics relative to an observer using the gravitational path integral. We apply our proposal to an observer that lives in a closed universe and one that falls behind a black hole horizon. We find that the Hilbert space that describes the experience of the observer is much larger than the Hilbert space in the absence of an observer. In the case of closed universes, the Hilbert space is not one-dimensional, as calculations in the absence of the observer suggest. Rather, its dimension scales exponentially with ${G}_{N}^{-1}$. Similarly, from an observer’s perspective, the dimension of the Hilbert space in a two-sided black hole is increased. We compute various observables probing the experience of a gravitating observer in this Hilbert space. We find that an observer experiences non-trivial physics in the closed universe in contrast to what it would see in a one-dimensional Hilbert space. In the two-sided black hole setting, our proposal implies that non-perturbative corrections to effective field theory for an infalling observer are suppressed until times exponential in the black hole entropy, resolving a recently-raised puzzle in black hole physics. While the framework that we develop is exemplified in the toy-model of JT gravity, most of our analysis can be extended to higher dimensions and, in particular, to generic spacetimes not admitting a conventional holographic description, such as cosmological universes or black hole interiors.

2D gravity↗

Path integral factorization and the gravitational effective action

Abstract We discuss the factorization and continuity properties of fields in the Euclidean gravitational path integral with higher dimension operators constructed from powers of the Riemann tensor. We construct the boundary terms corresponding to the microcanonical ensemble and show that the saddle point approximation to the path integral with a quasilocal energy constraint generally yields a saddle point with discontinuous temperature. This extends a previous result for the Euclidean Schwarzschild–de Sitter geometry in Einstein gravity and shows that it is robust against at least some types of quantum corrections from heavy fields. As an application, we compute the entropy of SdS in D = 4 using the BTZ method. Our result matches the entropy calculated using Wald’s formula.

Astronomy & Astrophysics↗

The wavefunction of a quantum S 1 × S 2 universe

We study quantum gravity corrections to the no-boundary wavefunction describing a universe with spatial topology S 1 × S 2 . It has been suggested that quantum effects become increasingly important when the size of the circle is large relative to the sphere. In this paper, we confirm this claim by an explicit four-dimensional one-loop calculation of the gravitational path integral preparing such a state. In the process, we clarify some aspects of the gravitational path integral on complex spacetimes. These quantum corrections play a crucial role in ensuring that the norm of the wavefunction is naturally expressed in terms of a path integral over S 2 × S 2 at the classical level. We extend some of the analysis to more general spatial topologies, as well as to the inclusion of fermions.

cosmological models↗

Holography: Quantum Mechanical Aspects of Black Holes (Final Report)

Current theories of fundamental physics are based on quantum field theory, unifying quantum mechanics and special relativity. A similar unification of quantum field theory with gravity has been elusive. String theory is a consistent model of quantum gravity and it is important to identify general lessons that can be applied to the real world. The main technique that emerged from such studies has been the gravitational path integral. During the period of this grant, the PI has explored the implication of the gravitational path integral in novel setups to uncover new features of rotating black holes in four dimensions, as well as increasing our understanding of some specific black holes in string theory.

79 ASTRONOMY AND ASTROPHYSICS↗

Living on the edge: a non-perturbative resolution to the negativity of bulk entropies

Lin, Maldacena, Rozenberg, and Shan (LMRS) presented a new information paradox in black hole physics by noticing that the entanglement and Rényi entropies in a two-sided black hole can become negative when the geometry contains a very large number of matter excitations behind the black hole horizon. While originally this puzzle was presented in the context of BPS two-sided black holes in two-dimensional supergravity, the negativity in fact persists for more general two-sided black holes in the presence of a large number of matter excitations. Since the entanglement and Rényi entropies in ordinary quantum systems cannot be negative, resolving this puzzle is a necessary step towards understanding the quantum mechanical description of black holes. In this paper, we explain how to address the entanglement negativity puzzle, both in the original setting discussed by LMRS and in more general non-supersymmetric settings, by summing over all non-perturbative contributions to the gravitational path integral. We then interpret this result from the point of view of a dual matrix integral, which we use to extend our analysis beyond the regime of validity of the genus re-summation performed in the gravitational path integral. In this regime, positivity is rescued by new saddles of the matrix integral, a one-eigenvalue instanton and a two-eigenvalue instanton. Finally, we formulate a similar puzzle and its resolution using random tensor network techniques.

2D Gravity↗

Living on the edge: a non-perturbative resolution to the negativity of bulk entropies

Lin, Maldacena, Rozenberg, and Shan (LMRS) presented a new information paradox in black hole physics by noticing that the entanglement and Rényi entropies in a two-sided black hole can become negative when the geometry contains a very large number of matter excitations behind the black hole horizon. While originally this puzzle was presented in the context of BPS two-sided black holes in two-dimensional supergravity, the negativity in fact persists for more general two-sided black holes in the presence of a large number of matter excitations. Since the entanglement and Rényi entropies in ordinary quantum systems cannot be negative, resolving this puzzle is a necessary step towards understanding the quantum mechanical description of black holes. In this paper, we explain how to address the entanglement negativity puzzle, both in the original setting discussed by LMRS and in more general non-supersymmetric settings, by summing over all non-perturbative contributions to the gravitational path integral. We then interpret this result from the point of view of a dual matrix integral, which we use to extend our analysis beyond the regime of validity of the genus re-summation performed in the gravitational path integral. In this regime, positivity is rescued by new saddles of the matrix integral, a one-eigenvalue instanton and a two-eigenvalue instanton. Finally, we formulate a similar puzzle and its resolution using random tensor network techniques.

FOS: Physical sciences↗

Spin-statistics for black hole microstates

The gravitational path integral can be used to compute the number of black hole states for a given energy window, or the free energy in a thermal ensemble. In this article we explain how to use the gravitational path integral to compute the separate number of bosonic and fermionic black hole microstates. We do this by comparing the partition function with and without the insertion of (–1) F . In particular we introduce a universal rotating black hole that contributes to the partition function in the presence of (–1) F. We study this problem for black holes in asymptotically flat space and in AdS, putting constraints on the high energy spectrum of holographic CFTs (not necessarily supersymmetric). Finally, we analyze wormhole contributions to related quantities.

79 ASTRONOMY AND ASTROPHYSICS↗

Do holographic CFT states have unique semiclassical bulk duals?

Here, we discuss a situation where a holographic CFT state has multiple semiclassical bulk duals. In our example, a given holographic state has two simple, semiclassical descriptions, one with a closed universe, constructed using the gravitational path integral, and one without a closed universe, constructed using the extrapolate dictionary. This highlights an ambiguity in the AdS/CFT dictionary. We propose various options for resolving this tension although none is perfectly satisfactory. We also discuss what this implies for the black hole interior and the gravitational path integral.

AdS/CFT correspondence↗

Quantum mechanics and observers for gravity in a closed universe

Recent arguments based on the quantum extremal surface formula or the gravitational path integral have given fairly compelling evidence that the Hilbert space of quantum gravity in a closed universe is one-dimensional and real. How can this be consistent with the complexity of our own experiences? In this paper we propose that the experiences of any observer Ob in a closed universe can be approximately described by a quantum mechanical theory with a Hilbert space whose dimension is roughly e S Ob , where S Ob is the number of degrees of freedom of Ob. Moreover we argue that the errors in this description are exponentially small in S Ob . We give evidence for this proposal by incorporating it into the gravitational path integral and the coding interpretation of holography in simple models and seeing that it works, and we explain how similar effects arise in black hole physics in appropriate circumstances.

AdS-CFT Correspondence↗

Null states and time evolution in a toy model of black hole dynamics

Abstract Spacetime wormholes can provide non-perturbative contributions to the gravitational path integral that make the actual number of statese S in a gravitational system much smaller than the number of states$$ {e}^{S_{\textrm{p}}} $$ e S p predicted by perturbative semiclassical effective field theory. The effects on the physics of the system are naturally profound in contexts in which the perturbative description actively involvesN=O(e S ) of the possible$$ {e}^{S_{\textrm{p}}} $$ e S p perturbative states; e.g., in late stages of black hole evaporation. Such contexts are typically associated with the existence of non-trivial quantum extremal surfaces. However, by forcing a simple topological gravity model to evolve in time, we find that such effects can also have large impact forN≪e S (in which case no quantum extremal surfaces can arise). In particular, even for smallN, the insertion of generic operators into the path integral can cause the non-perturbative time evolution to differ dramatically from perturbative expectations. On the other hand, this discrepancy is small for the special case where the inserted operators are non-trivial only in a subspace of dimensionD≪e S . We thus study this latter case in detail. We also discuss potential implications for more realistic gravitational systems.

Physics↗

Mind the crosscap: $τ$-scaling in non-orientable gravity and time-reversal-invariant systems

Spectral statistics of quantum chaotic systems are governed by random matrix universality. In many cases of interest, time-reversal symmetry selects the Gaussian Orthogonal Ensemble (GOE) as the relevant universality class. In holographic CFTs, this is mirrored by the presence of non-orientable geometries in the dual gravitational path integral. In this work, we analyze general properties of these matrix models and their gravitational counterparts. First, we develop a formalism to express the universal level statistics in the canonical ensemble for arbitrary spectral curves, leading to a topological expansion with finite radius of convergence in the late-time $τ$-scaling limit. Then, we focus on topological gravity and study topological recursion on the moduli space of non-orientable surfaces. We find that the Weil-Petersson volumes display non-analytic behaviour multiplying polynomials in the boundary lengths. The volumes give rise to wormholes with late-time divergences, in contrast with the orientable case, which is finite. We identify systematic cancellations among WP volumes implied by the consistency and finiteness of the $τ$-scaling limit. In particular, the cancellation of late-time divergences requires a nontrivial genus resummation. Working in the gravitational microcanonical ensemble, we derive and resum all orders of the topological expansion matching the GOE matrix model in the high-energy regime.

Chaotic Dynamics (nlin.CD)↗

Path integral suppression of badly behaved causal sets

Abstract Causal set theory is a discrete model of spacetime that retains a notion of causal structure. We understand how to construct causal sets that approximate a given spacetime, but most causal sets are not at all manifold-like, and must be dynamically excluded if something like our Universe is to emerge from the theory. Here we show that the most common of these ‘bad’ causal sets, the Kleitman–Rothschild orders, are strongly suppressed in the gravitational path integral, and we provide evidence that a large class of other ‘bad’ causal sets are similarly suppressed. It thus becomes plausible that continuum behavior could emerge naturally from causal set quantum theory.

Astronomy & Astrophysics↗

BPS and near-BPS black holes in AdS 5 and their spectrum in $\mathcal{N}$ = 4 SYM

We study quantum corrections in the gravitational path integral around nearly 1/16-BPS black holes in asymptotically AdS 5 × S 5 space, dual to heavy states in 4D N = 4 super Yang-Mills. The analysis provides a gravitational explanation of why 1/16-BPS black holes exhibit an exact degeneracy at large N and why all such states have the same charges, confirming the belief that the superconformal index precisely counts the entropy of extremal black holes. We show the presence of a gap of order N −2 between the 1/16-BPS black holes and the lightest near-BPS black holes within the same charge sector. This is the first example of such a gap for black hole states within the context of AdS 5 holography. We also derive the spectrum of near-BPS states that lie above this gap. Our computation relies on finding the correct version of the N = 2 super-Schwarzian theory which captures the breaking of the SU(1, 1|1) symmetry when the black hole has finite temperature and non-zero chemical potential. Finally, we comment on possible stringy and non-perturbative corrections that can affect the black hole spectrum.

AdS-CFT Correspondence↗

Complex saddles and Euclidean wormholes in the Lorentzian path integral

We study complex saddles of the Lorentzian path integral for 4D axion gravity and its dual description in terms of a 3-form flux, which include the Giddings-Strominger Euclidean wormhole. Transition amplitudes are computed using the Lorentzian path integral and with the help of Picard-Lefschetz theory. The number and nature of saddles is shown to qualitatively change in the presence of a bilocal operator that could arise, for example, as a result of considering higher-topology transitions. We also analyze the stability of the Giddings-Strominger wormhole in the 3-form picture, where we find that it represents a perturbatively stable Euclidean saddle of the gravitational path integral. This calls into question the ultimate fate of such solutions in an ultraviolet-complete theory of quantum gravity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Black Hole Airy Tail

In Jackiw-Teitelboim (JT) gravity, which is dual to a random matrix ensemble, the annealed entropy differs from the quenched entropy at low temperatures and goes negative. However, computing the quenched entropy in JT gravity requires a replica limit that is poorly understood. To circumvent this, we define an intermediate quantity called the semiquenched entropy, which has the positivity properties of the quenched entropy, while requiring a much simpler replica trick. We compute this in JT gravity in different regimes using (i) a bulk calculation involving wormholes corresponding to the Airy limit of the dual matrix integral and (ii) a boundary calculation involving one-eigenvalue instanton saddles proposed by Hernández-Cuenca, demonstrating consistency between these two calculations in their common regime of validity. We also clarify why similar one-eigenvalue instanton saddles cannot be used to compute the quenched entropy due to a breakdown of the saddle-point approximation for the one-eigenvalue instanton in the replica limit. Our results show how to use the gravitational path integral to prove that black holes in JT gravity have isolated ground states and to study their properties.

Gauge-gravity dualities↗